I always thought it was shocking at the end of American History X that Derek didn't leave Los Angeles and possibly take his family with him. I was under the impression that, after he got out of prison, the black gangs would be trying to get revenge on him for killing two of their members.

To make things worse, he beats up Cameron the night he gets out, and everybody in the white supremacist camp knows about it - one of them (his friend) even tries to shoot him as he's leaving the party. He even mentions a couple times that he thinks he's in mortal danger.

How is he able to walk around in broad daylight without seeming overly concerned for his own safety or that of Danny?

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The total timeline of events is really, really short. Danny gets assigned the paper for Dr. Sweeney on the morning of Derek's release. He gets killed prior to turning in the paper the very next morning. So, all of those events happened in a single evening.

Furthermore, I never got the impression that Derek was aware of the initial 'smoke in the face' incident that led to the film's conclusion, but was still escorting Danny to school for safety (due to the previous night's events) while he figured out what he was going to do.